Abstract. For a very general class of probability distributions in disordered
Ising spin systems, in the thermodynamical limit, we prove the following
property for overlaps among real replicas. Consider the overlaps among s
replicas. Add one replica s+1. Then, the overlap q(a,s+1) between one of
the first s replicas, let us say a, and the added s+1 is either independent
of the former ones, or it is identical to one of the overlaps q(a,b),
with b running among the first s replicas, excluding a. Each of these
cases has equal probability 1/s.